Moser iteration applied to elliptic equations with critical growth on the boundary

By Greta Di Marino, Patrick Winkert. Nonlinear Analysis, 2018

50 citations recorded by the source corpus.

This paper deals with boundedness results for weak solutions of an elliptic equation where the functions are Caratheodory functions satisfying certain $p$-structure conditions that have critical growth even on the boundary. Based on a modified version of the Moser iteration we are able to prove that every weak solution of our problem is bounded up to the boundary. Under some additional assumptions this leads directly to $C^{1,\alpha}$-regularity for weak solutions of the problem.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/17109f4df8f1117d4b8564e0ef210e4c944d875a

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In Applied Mathematics

In Computational Theory and Mathematics

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Citations in the corpus

New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, result): “We also mention the boundedness results in the works of Barletta-Cianchi-Marino [4] (for problems in Orlicz spaces), Gasiński-Winkert [33, 35] (for double phase Dirichlet and Neumann problems), Ho-Sim [40] (for weighted problems), Kim-Kim-Oh-Zeng [44] (for variable exponent double phase problems wit”
Constant sign solutions for double phase problems with superlinear nonlinearity (2019, methodology): “1) which are based on the recent work of MarinoWinkert [18] by applying Moser’s iteration.”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, methodology): “1) following the treatment of Marino-Winkert [30], see Theorem 3.”